x^2-12=-11x

Solution for x^2-12=-11x equation:

x^2-12=-11x

We move all terms to the left:

x^2-12-(-11x)=0

We get rid of parentheses

x^2+11x-12=0

a = 1; b = 11; c = -12;
Δ = b2-4ac
Δ = 112-4·1·(-12)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-13}{2*1}=\frac{-24}{2}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+13}{2*1}=\frac{2}{2}
=1
$